Lesson 12: From Ratio Tables to Double Number Line … 12: From Ratio Tables to Double Number Line...

Lesson 12: From Ratio Tables to Double Number Line Diagrams Date: 4/1/14

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NYS COMMON CORE MATHEMATICS CURRICULUM 6•1 Lesson 12

Lesson 12: From Ratio Tables to Double Number Line

Diagrams

Student Outcomes

Students create equivalent ratios using a ratio table and represent these ratios on a double number line

diagram.

Students extend and use a double number line diagram to solve ratio problems related to the real world.

Classwork

Exercise 1 (5 minutes)

Recall of prior knowledge—Ratio Tables (See attached ratio cards.)

Each student is given a card with a ratio on it. The students move around the room in

search of other students who have ratios that are equivalent to theirs. Students with

equivalent ratios will form a group and create a ratio table, which will contain all of the

equivalent ratios. As students present their ratio tables, the student audience will

determine the accuracy of the groups’ formations, as well as their tables. Circulate the

room as a facilitator, guiding students who are having trouble. Collect cards and direct

students back to their seats once the groups are completed.


A guided whole-group discussion occurs as outlined below. Students are given time to

think about and discuss the following questions independently and/or with their peers and

then contribute to the whole-group discussion.

Exercise 2

The amount of sugary beverages Americans consume is a leading health concern. For a given brand of cola, a 12-ounce

serving of cola contains about 40 grams of sugar. Complete the ratio table, using the given ratio to find equivalent ratios.

Answers may vary but are found by either multiplying or dividing both 12 and 40 by the same number.

Cola (ounces) 6 12 18

Sugar (grams) 20 40 60

Scaffolding:

Differentiate the activity by

choosing select cards for each

student. A ratio of 2:1 may be

easier for a struggling learner

to conceptualize, while a ratio

of 3

: 2 may be more

challenging.

MP.2

For more support:

To provide more information

on this topic to support all

learners’ needs, refer to

Teacher Notes - More

Information on Soda and Sugar

for video and news-related

links.

http://creativecommons.org/licenses/by-nc-sa/3.0/deed.en_US


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Fluency Exercise to Reinforce

Understanding:

Students can practice skip-

counting aloud for each

number line to understand the

concept of scale.


Exercise 3

A 1-liter bottle of cola contains approximately 34 fluid ounces. How many grams of sugar would be in a 1-liter bottle of

the cola? Explain and show how to arrive at the solution.

Cola (ounces) 6 12 18 30 36

Sugar (grams) 20 40 60 100 120

Students may use different approaches. Some students may decide to extend their tables but may realize that they do

not “easily” arrive at 34 for the ounces of cola when finding equivalent ratios. After adequate time, have

students/groups present their predictions and methods to the class.

When eliciting students’ responses, ask probing questions as the opportunity arises, (i.e.: “So are you telling me that

since 34 ounces is between 30 and 36 ounces, the answer will be between 100 and 120 grams of sugar? Is it closer to

100 or 120? How do you know? Will the answer be a whole number? Why or why not? Can you express your answer

as a mixed number?”)

What are some of the challenges we face when using a table for this type of problem?

34 is not a multiple of 6, and we are counting by 6’s for the ounces of cola and by 20’s for grams of

sugar.

Example 1 (9 minutes)

Whole group instruction continues with a teacher-led illustration of using a double number

line diagram to arrive at the answer for Example 1. Discussion includes the need for two

different number lines since we are comparing ounces and grams, which are not the same

units (1 gram is not equivalent to 1 ounce). Students record the following illustration on

the double number line reproducible.

What is the scale we are using on each number line?

6 for cola and 20 for sugar

MP.3

MP.1

MP.5

0 6 12 18 24 30 34 36 cola (ounces)

0 20 40 60 80 100 ? 120 sugar (grams)



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Show on the cola number line that 34 ounces is

or

of the way between 30 and 36. The answer for grams of sugar

will be

or

of the way between 100 and 120. Since the intervals are by 20, to determine the answer, find

of 20 and

add it to 100. Students may choose to use

instead of

.

Elicit student volunteers to show the math process and work using each of the two fractions. Students should see that

the answers will be the same regardless of which fraction was used.

OR

grams of sugar

grams of sugar


Exercise 4

A school cafeteria has a restriction on the amount of sugary drinks available to students. Drinks may not have more than

25 grams of sugar. Based on this restriction, what is the largest size cola (in ounces) the cafeteria can offer to students?

My estimate is between 6 and 12 ounces but closer to 6 ounces. I need to find ¼ of 6 and add it to 6.

A

ounce cola is the largest size that the school cafeteria can offer to students.

After students have ample time to create their double number line diagram and answer the question, encourage

students to present their thought process to the class.

0 6 ? 12 18 cola (ounces)

0 20 40 60 sugar (grams)

25 30 35



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Exercise 5 (time permitting)

Exercise 5

Shontelle solves three math problems in four minutes.

a. Use this information to complete the table below.

b. Shontelle has soccer practice on Thursday evening. She has a half hour before practice to work on her math

homework and to talk to her friends. She has 20 math skill-work questions for homework, and she wants to

complete them before talking with her friends. How many minutes will Shontelle have left after completing

her math homework to talk to her friends?

Use a double number line diagram to support your answer, and show all work.

Closing (5 minutes)

Have students complete the 3-2-1 Activity.

Name three different ways you can represent a group of equivalent ratios.

Ratio Table, Tape Diagram, Double Number Line Diagrams

Share two things you learned about Double Number Line Diagrams.

Tell one thing you want to know more about from today’s lesson.

Exit Ticket (5 minutes)

Number of

Questions 3 6 9 12 15 18 21 24 27 30

Number of

Minutes 4 8 12 16 20 24 28 32 36 40

Step 1:

Step 2:

Step 3:

Shontelle can talk to her friends for

minutes.

Lesson Summary

Double Number Line Diagram: a tool used for understanding the equivalence of two related numbers. It is called

“double” because each mark on the line has two numbers matched to it. The top row of numbers describes the

whole represented by the line in one way, and the bottom row describes the whole represented by the line in

another way. Because the whole line is the same, it is possible to see the equivalences between the rows of

numbers at any point on the line.



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Additional Teacher Notes

More Information on Soda and Sugar:

Video: http://www.cnn.com/2013/01/14/health/coke-obesity

Video: http://www.teachertube.com/viewVideo.php?video_id=13788

http://www.sugarstacks.com/beverages.htm

http://www.cdc.gov/features/healthybeverages/


http://www.cnn.com/2013/01/14/health/coke-obesity

http://www.teachertube.com/viewVideo.php?video_id=13788

http://www.sugarstacks.com/beverages.htm

http://www.cdc.gov/features/healthybeverages/


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Name ___________________________________________________ Date____________________

Lesson 12: From Ratio Tables to Double Number Line Diagrams

Exit Ticket

Kyra is participating in a fundraiser Walk-a-Thon. She walks 2 miles in 30 minutes. If she continues to walk at the same

rate, determine how many minutes it will take her to walk 7 miles. Use a double number line diagram to support your

answer.



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Exit Ticket Sample Solution

The following solutions indicate an understanding of the objectives of this lesson:

Kyra is participating in a fundraiser Walk-a-Thon. She walks 2 miles in 30 minutes. If she continues to walk at the same

rate, determine how many minutes it will take her to walk 7 miles. Use a double number line diagram to support your

answer.

Miles

Minutes

It will take Kyra 105 minutes to walk 7 miles.

Problem Set Sample Solutions

1. While shopping, Kyla found a dress that she would really like, but it costs $52.25 more than she has. Kyla charges

$5.50 an hour for babysitting. She wants to figure out how many hours she must babysit to earn $52.25 to buy the

dress. Use a double number line to support your answer.

9.5 hours

2. Frank has been driving at a constant speed for 3 hours, during which time he traveled 195 miles. Frank would like to

know how long it will take him to complete the remaining 455 miles, assuming he maintains the same constant

speed. Help Frank determine how long the remainder of the trip will take. Include a table or diagram to support

your answer.

7 hours

2 4 6 7 8

30 60 90 105 120



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7 to 4 28:16 3

to 2 35:20

3 to 8 30:80 6 to 16 12:32

5 to 1 45:9 15 to 3 2

to



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3 to 4 9:16 1

to 2 15:20

3 to 6 30:60 1 to 2 4:8

2 to 1 44:22 18:9 1 to



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1 to 6 8:48 6 to 36 5:30

9 to 4 36:16 3 to

18:8

7 to 6 42:36 21 to 8 3

to 3



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Double Number Line Reproducible


Lesson 12: From Ratio Tables to Double Number Line … 12: From Ratio Tables to Double Number Line...

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